A finite group L is said to
be quasisimple if L = L′ and L∕Z(L) is simple and is said to be 2-quasisimple if
L = L′ and L∕O(L) is quasisimple. Let G denote a finite group. Then E(G)
is the subgroup of G generated by all subnormal quasisimple subgroups
of G and F∗(G) = E(G)F(G) where F(G) is the Fitting subgroup of G.
Also a subnormal quasisimple subgroup of G is called a component of G
and a subnormal 2-quasisimple subgroup of G is called a 2-component of
G.